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6th Edition

Stewart + 5 others

Publisher: Cengage Learning

ISBN: 9780840068071

Chapter 1.7, Problem 3E

(**a**)

To determine

**To fill:** The blank in the statement “The solution of the inequality

Expert Solution

The complete statement is “The solution of the inequality

**Property used:**

*Properties of absolute value inequalities:*

Inequality | Equivalent form |

**Calculation:**

The given inequality is

This is of the form

Then by the properties mentioned above, the given inequality is equivalent to

Note that, here both the end points are included since the inequality sign is

Then, the solution will be a closed interval. That is,

Thus, the complete statement is “The solution of the inequality

(**b**)

To determine

**To fill:** The blank in the statement “The solution of the inequality

Expert Solution

The complete statement is “The solution of the inequality

The given inequality is

This is of the form

Then by the properties mentioned in part (**a**), the given inequality is equivalent to

That is, the solution of the given inequality is the union of the set of all points that are less than or equal to

Note that, here both the end points are included since the inequality sign is

The set of all points that are less than or equal to

Thus, the complete statement is “The solution of the inequality